Questions: A nation's population is growing at a rate of 0.7% annually. In how many years will the population double? 100 140 50 20

Transcript text: Question 17 1 pts A nation's population is growing at a rate of $0.7 \%$ annually. In how many years will the population double? 100 140 50 20

Solution

Solution Steps

To determine how many years it will take for a population to double given a constant annual growth rate, we can use the Rule of 70. This rule states that you can estimate the doubling time by dividing 70 by the annual growth rate percentage.

Step 1: Determine the Doubling Time Formula

To find the time $ t $ required for a population to double at an annual growth rate $ r $, we can use the formula derived from the Rule of 70: \[ t \approx \frac{70}{r} \]

Step 2: Substitute the Growth Rate

Given the annual growth rate $ r = 0.7\% $, we convert this percentage to a decimal for calculation: \[ r = 0.7 = 0.007 \] Now, substituting $ r $ into the formula: \[ t \approx \frac{70}{0.7} = 100 \]

Step 3: Conclusion

The calculated doubling time is $ 100 $ years.